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The paper addresses consensus-based networked estimation of the state of a nonlinear dynamical system. The focus is on a family of distributed state estimation algorithms which relies on the extended Kalman filter linearization paradigm. Consensus is exploited in order to fuse the information, both prior and novel, available in each network node. It is shown that the considered family of distributed Extended Kalman Filters enjoys local stability properties, under minimal requirements of network connectivity and system collective observability. A simulation case-study concerning target tracking with a network of nonlinear (angle and range) position sensors is worked out in order to show the effectiveness of the considered nonlinear consensus filter.